Sen. Ted Cruz of Texas said in a radio interview Friday that Ohio Gov. John Kasich has no plausible path to the GOP presidential nomination and that voters who support Mr. Kasich in Utah this Tuesday would effectively be boosting Republican front-runner Donald Trump.

Mr. Cruz pointed out that a candidate who breaks 50 percent of the vote in Utah’s GOP caucuses on Tuesday wins all 40 of the state’s delegates. If no candidate cracks 50 percent, the delegates are allocated proportionally, with a 15-percent minimum threshold for winning any delegates.

“We still have a direct path to 1,237 delegates,” Mr. Cruz said on KSL, a Utah-based station. “In any scenario, John Kasich has no plausible path, and I’ll tell you in the state of Utah, the reality is straightforward. A vote for John Kasich is a vote for Donald Trump, because right now Kasich on the ballot is just dividing votes [of] the opposition to Donald Trump.”

“And if Kasich manages to pull enough votes in Utah to pull me below 50 percent, the effect of John Kasich will be giving Donald Trump 20 more delegates, which I think would be a big, big mistake,” Mr. Cruz said.

“And so if you want to stop Donald Trump, there is only one campaign and only one candidate who has done so repeatedly and who has any plausible path to do so,” he said. “For Kasich, it’s mathematically impossible.”

Sen. Marco Rubio had tried to make a similar pitch in Florida before Mr. Rubio’s devastating loss in Tuesday’s primary, saying a vote for either Mr. Kasich or Mr. Cruz would effectively be a vote for Mr. Trump, since Mr. Rubio was closest to the front-runner in polling in the winner-take-all state.

A Kasich campaign spokesman fired back that a vote for Mr. Cruz is actually a vote for Democratic presidential front-runner Hillary Clinton.

“Given the fact that Ted Cruz loses to Hillary Clinton while we beat her, a vote for Ted Cruz is actually a vote for Hillary,” spokesman Rob Nichols said in an email.

In an earlier appearance on the station, Mr. Kasich said it’s still too early to definitively predict what’s going to happen.

“Under the rules of the convention, if you don’t get enough delegates, you don’t get nominated unless you can accumulate enough,” Mr. Kasich said. “So I don’t sort of think down the road — oh, I have this strategy to go to a convention. My whole deal is I can help run this country. I’m the only one that can beat Hillary Clinton, and we’ll see where it goes, because things are so crazy, you just never know.”

“I could end up having the most amount of delegates going into the convention — who knows?” Mr. Kasich said. “Take things a day at a time.”